How long will it take a car traveling at 60 mph to overtake a bus traveling at 40 mph if the bus had a 1.5 hour head start?
Distance D = Rate R * Time T
60 = rate for car
T = time for car
60T = distance for car
40 = rate for bus
T + 1.50 = rate for bus
40(T + 1.50) = distance for bus
Distances are equal
60T = 40(T + 1.50)
Solve for T, time in hours for car to overtake the bus
R + 40 = rate for train
At the point of overtaking they must have gone the same distance, d
then the difference in their times must have been 1.5 hrs.
d/40 - d/60 = 1.5
times 120
3d - 2d = 180
d = 180
can you take it from there?
Ignore this line from my post above,
"R + 40 = rate for train"
25
To determine how long it will take the car to overtake the bus, we need to consider their relative speeds and the head start of the bus.
Step 1: Calculate the distance traveled by the bus during its head start.
The distance is equal to the speed of the bus multiplied by the time it traveled:
Distance = Speed × Time
Distance = 40 mph × 1.5 hours = 60 miles
Step 2: Calculate the relative speed of the car with respect to the bus.
Since the car is trying to catch up, we need to subtract the speed of the bus from the speed of the car:
Relative Speed = Car's Speed - Bus's Speed
Relative Speed = 60 mph - 40 mph = 20 mph
Step 3: Calculate the time it will take for the car to cover the distance traveled by the bus.
We divide the distance by the relative speed of the car:
Time = Distance / Relative Speed
Time = 60 miles / 20 mph = 3 hours
Therefore, it will take the car 3 hours to overtake the bus.